On Whitehead's cut vertex lemma
Abstract
One version of Whitehead's famous cut vertex lemma says that if an element of a free group is part of a free basis, then a certain graph associated to its conjugacy class that we call the star graph is either disconnected or has a cut vertex. We state and prove a version of this lemma for conjugacy classes of elements and convexcocompact subgroups of groups acting cocompactly on trees with finitely generated edge stabilizers.
 Publication:

arXiv eprints
 Pub Date:
 May 2022
 DOI:
 10.48550/arXiv.2205.06071
 arXiv:
 arXiv:2205.06071
 Bibcode:
 2022arXiv220506071A
 Keywords:

 Mathematics  Group Theory;
 Mathematics  Geometric Topology;
 20F65;
 20E08;
 20E36
 EPrint:
 8 pages, 2 figures